Here, \(\eta \)  is a user-selected parameter with a common choice \(\eta = 0.8\) ; see, e.g., [1]}.
This strategy adaptively picks BB1 and BB2 steps based on the value of \(\beta _{k}^{\rm {BB2}} / \beta _{k}^{\rm {BB1}} = \cos ^2(\mathbf {s}_{k-1}, \mathbf {y}_{k-1})\) .
